Stifling: Passengers were trapped in carriages with staff refusing to open the doors for security reasons

Furious passengers told today how their Eurostar journeys were delayed by up to 13 hours after migrants trespassed on tracks and clambered on to train roofs.

Two trains were cancelled today after six were hit by the chaos last night, as the British and other EU governments came under growing pressure to get a grip on Europe’s escalating migrant crisis. Its shocking death toll, with thousands having already drowned in the Mediterranean, climbed higher today.

At least 11 more migrants, believed to be Syrians, drowned as two boats sank after leaving south-west Turkey for the Greek island of Kos. Tens of thousands of migrants a week are arriving in Greece and heading west.

In Hungary thousands remained stranded at Budapest’s international railway station as the authorities stuck to European Union rules and prevented them leaving for Germany and other EU countries including the UK.

After security was tightened at the Eurotunnel entrance near Calais, migrants tried to get on to trains further down the tracks last night.

Rescue: Passengers wrapped in thermal foil blankets given out by emergency services after their Eurostar train was stranded at Calais Station

The intrusions led to the network being shut down and Eurostar passenger services through the tunnel stopped as police tried to clear the trespassers.

Passengers were stuck for several hours and left in stifling conditions as staff refused to open the doors for security reasons. Police finally arrived at the scene just before midnight to remove the trespassers, who had been seen climbing on top of trains.

Two trains were forced to turn back in the early hours — one to Paris, one to London. But a second London-bound train that had been held in Calais and tried to begin its journey suffered a mechanical failure, with passengers left in the freezing cold for hours until a rescue train arrived at 9am — two hours after it was first scheduled to do so.

Passengers were finally on the move at 9.35am and were expected back in London at just before 11am.

Up to 2,000 travellers are believed to have been affected by the disruption to Eurostar services.

Dozens of passengers were left stranded at Calais

Public relations executive Simon Gentry, who went to Paris yesterday for a two-hour meeting, was caught up in the delays and was set to arrive back in London today nearly 13 hours late. “It has all been a fiasco and totally exhausting,” said Mr Gentry, 48, from Chiswick. “When Eurostar first said there were delays because of migrants, everyone felt somewhat sympathetic.

“We were then given to believe the migrants had damaged the train, which meant we could not leave. They turned off the air conditioning and it became stifling, smelly and really disgusting.

“At 4am they told us a train would be arriving to take us back to London. We got pulled to a station outside Calais at about 6am and told to get off. We were then herded around before being told the rescue train was delayed.

Closure: Migrants stand in the main Eastern Railway station in Budapest, which was shut to trains on Tuesday

“It is just stupid. Tell people what the situation is and they will deal with it. But if you raise people’s expectations and then let them down they will get cross.” Eurostar initially claimed the rescue train would arrive at 7am but it was in fact delayed by two hours, meaning it only left Calais at 9.35am.

A spokesman said the company had to balance rescuing the passengers with not creating another knock-on effect to its service. He added: “The tunnel is very busy. There are not just our trains. Our priority is to make sure our operation is strong and resilient.”

But passenger Tom Mayes branded Eurostar’s handling of the situation as “pathetic”, tweeting: “Children here hungry and thirsty. 12hrs, no food and limited water.” Fellow traveller Fay Collett said their treatment had been “atrocious” and “inhumane”.

There was more misery this morning when the 7.55am train from St Pancras to Paris was cancelled.

Leonardo Severino, 43, who was travelling to Paris with his wife and two young children, said: “They have told us the next train is already fully occupied so we really don’t know how long we will have to be here.”

A queue of passengers snaked through St Pancras station this morning. The 11.13 Paris to London service was also cancelled.

EU interior ministers are to hold an emergency meeting on September 14 to discuss the migrant crisis, with Germany and other nations urging Britain to do more to deal with the hundreds of thousands of people fleeing Syria and other countries.

Former Belgian prime minister Guy Verhofstadt said on BBC radio: “You need a common asylum system and a burden-sharing. You cannot say that it is only the Italians, where they enter, or the Greeks, where they enter, or Germany, where they want to go, who is responsible for this enormous crisis.”